This project involved the measurement of adsorption equilibria using two techniques - gravimetric and volumetric techniques. 106 Figure 7 - 12: Experimental and predicted binary adsorption data for a binary mixture of ethane/ethylene on zeolite 13X at 323 K and 1.378 bar. 111 Figure 7 - 17: Experimental and predicted binary adsorption data for binary mixture ethane/ethylene on zeolite 13X at 323 K and 1.378 bar.
Introduction
In the second step, the temperature of the bed is raised to T2 by passing hot feed or steam through it. This study investigated the use of adsorption techniques in the separation of the ethane/ethylene system. Research has also been conducted into the use of zeolite 13X for the separation of the ethane/ethylene system – the system examined in this study.
Adsorption Equilibria Fundamentals
- Adsorption Steps
- Forces of Adsorption
- Selectivity
- Thermodynamics of Adsorption
- Criterion for Equilibrium
- Isoteric Heat of Adsorption
- Partial Molar Entropy
- Adsorption Equilibrium Constant
The thermodynamic and geometric properties of the adsorbent are independent of temperature, pressure and gas composition. If the difference in the heat capacity of the gas in the adsorption and adsorbed phase is negligible, the isotheric heat of adsorption ∆𝐻𝑠 is given by:. The entropy change of the system in equilibrium ∆S is negative due to the reduction of the degrees of freedom.
Analysis, Modelling and Prediction of Adsorption Equilibria
Pure Gas Isotherms
- Langmuir Approach
- Langmuir Model
- Freundlich Model
- Langmuir-Freundlich Model (Sips Model)
- Gibbs Approach
- Potential Theory
Sticking probability is the probability that gas molecules are trapped on the surface of the adsorbent. As can be seen from Equations 3 - 8), the value of b decreases with increasing temperature, so physical adsorption is an exothermic process. There is considerable uncertainty in the methods used to estimate the molar volume of the adsorbed phase.
Gas Mixture Models
- Langmuir Approach
- Extended Langmuir Model
- Extended Langmuir-Freundlich (Sips) Model
- Gibbs Approach
- Potential Theory
A summary of the most commonly used models in the literature to regress and predict adsorption equilibria is presented in Table 3 - 1. 21 | P a g e The models presented in this chapter are the ones most frequently used in the literature. Brunauer–Emmett–Teller (BET), Dubinin-Polanyi, Dubinin-Radushkevich (DR), Ideal Adsorbed Solution Theory (IAST), Langmuir, Lattice Solution Model (LSM), Simplified Statistical Model of Thermodynamics (SSTM), Sips and Vacancy Solution Model (VSM) are among the models used in the literature.
A Review of the Techniques and Equipment used in the Measurement of Adsorption
Experimental Theory
A shortcoming of the Gibbs excess mass is the change of volume of the adsorbate phase. Argon was also used to determine the volume of the adsorbent (Keller et al., 1999). Statistical molecular models used to predict and simulate adsorption equilibria will generally result in the absolute mass of gas adsorbed and not the Gibbs excess mass as described in this chapter.
Experimental Techniques and Equipment
- The Volumetric Technique
- Gravimetric Technique
- Volumetric-Gravimetric Technique
- Oscillometric Technique
The pressure and temperature are measured and the gas volume in the presence of the adsorbent is calculated. The volume determined with the inert gas is the volume of the equilibrium gas phase Vg. Equilibrium is achieved when the mass of the sample in the adsorption chamber is constant.
Experimental Equipment and Procedure
Volumetric Apparatus
- Apparatus
- Equilibrium Cell
- The Storage Cell
- The Gas Mixing Cell
- Pressure, Temperature, Mass and Composition Measurements
- Valves, Fittings and Tubing
- Volumetric Experimental Method
- Leak Testing
- Calibrations
- Vapour Pressure Measurements
- Adsorbent preparation and loading
- System Volume
- Equilibrium Adsorption Measurements
- Operability and Safety of the Volumetric Apparatus
The amount of gas charged to the equilibrium cell is determined by measuring the change in pressure of the gas in the storage vessel. The pressure of the storage/mixture and the equilibrium cell was measured using WIKA D-10-P transducers. A second bath was used to maintain isothermal conditions of the storage cell and the mixture.
The pressure change of the gas in the storage cell was used to determine the number of moles loaded into the storage cell. At equilibrium, the pressure and temperature of the gas in the equilibrium cell were recorded. The mass of the gas loaded into the equilibrium cell was determined from the change in pressure of the gas in the storage cell.
After removal of volatile impurities and reaching equilibrium (indicated by constant pressure), the temperature (T2, T3) and pressure (P2) of the equilibrium cell were recorded. A needle valve, V4, was used to control the amount of helium filled in the storage cell. The initial temperature and pressure of the nutrient cell (Ti1,Pi1) and the equilibrium cell (Ti2, Ti3, Pi2) were recorded.
The binary mixture was loaded to the equilibrium cell using the same procedure as that of the pure component measurements.
Gravimetric Apparatus and Experimental method used in this study
- Intelligent Gravimetric Analyser (IGA)
- Gravimetric Experimental Method
- Leak testing and calibrations
- Equilibrium Adsorption Measurement
- Operability and Safety of the IGA
The rest of the measurement technique is as described for the pure component measurements with the addition of composition analysis. Valves V3, V5 and V8 were opened to evacuate the mixing cell and filling lines and closed upon completion of the evacuation step. V1 and V4 were closed when the desired amount of gas A was loaded into the mixing cell.
V2, V3 and V4 were closed when the desired amount of gas B was loaded into the mixing cell. The pump is manufactured with flexible stainless steel bellows for integration with the IGA gas handling system. The temperature of the reactor is maintained using a cooled recirculated water bath – up to 353 K, or an oven (not shown in the figure).
For further reading, the reader is referred to the IGA Systems User's Guide provided electronically with this dissertation. As mentioned in Chapter 4, this technique requires a mass of dry adsorbent. After the measurement of the isotherm, the gas cylinder was closed and the system was emptied.
The reader is referred to the IGA Manual for detailed operating procedures of the apparatus.
Experimental Results and Discussion
Vapour Pressure Measurement
- Propylene
- R134a
71 | P a g e The deviation of the experimental vapor pressure data for propylene from the extended Antoine predictions is presented below. The deviation of the experimental vapor pressure data for R134a from the extended Antoine predictions is presented below. The uncertainties in temperature and pressure reported in this study are comparable to those found in the literature.
Adsorption Measurements
- Pure component adsorption measurements
- Low Pressure Measurements
- High Pressure Measurements
- Binary Measurements
The experimental technique (volumetric) used in this study—adding incremental amounts of gas to the equilibrium cell—is susceptible to error in calculating the amount of gas adsorbed. Data from Loughlin et al. 1990) was used to validate the experimental method used in the high pressure range (up to 15 bar). The data measured by the volumetric technique in this study showed favorable comparisons with the literature. A graphical illustration of the experimental data is shown in Figures 6 - 5 , comparing the experimental data measured in this study with the literature data.
A graphical representation of the experimental data is shown in Figures 6 - 6 , comparing the experimental data measured in this study with the literature data. A graphical illustration of the experimental data is shown in Figures 6–7 and compares the experimental data measured in this study with the literature data. A graphical illustration of the experimental data is shown in Figures 6–8 and compares the experimental data measured in this study with the literature data.
This greater capacity is a result of the much smaller sample size used in the gravimetric technique. A graphical illustration of the experimental data is shown in Figure 6 - 9 and compares the experimental data measured in this study with literature data. Adsorption measurements of the binary system of ethane and ethylene were performed using the gas mixer in the experimental setup.
The experimental uncertainty in the gas phase composition, y, has a single contribution: the uncertainty arising from the calibration of the FID.
Modelling Adsorption Equilibria
Verification of the Models used for the Regression of the Measured Data
- The Langmuir Model
- The Sips Model
- The Vacancy Solution Model (VSM)
93 | P a g e The simplicity of Langmuir model ie. the ability to linearize the model and then solve for the model parameters using linear regression makes the model appealing. In this study, data from Pakseresht et al. 2002) were correlated using the Langmuir model in its non-linear form. Nonlinear regression was used to determine parameters of the Langmuir model for data from Nam et al.
2011) for the adsorption of ethane on activated carbon were correlated using the Langmuir model in its non-linear form. Tzabar et al (2011) used the Langmuir model in the linear form and this is perhaps the reason for the better fit obtained in this study. The experimental data along with regressed fits are presented in Figures 7 - 4. The parameters determined in this study were close to, but not identical to, those of Pakseresht et al.
The same tendency was observed when the data of Pakseresht et al. 2002) was regressed using the MATLAB code written in this study. The data of Kaul (1987) and Mofarahi and Salehi (2013) were used to verify the MATLAB code written in this study for the VSM model. The model parameters obtained in this study and those reported in the literature are shown in Table 7 - 5.
The model parameters obtained in this study and those of Mofarahi and Salehi (2013) are presented in Table 7–6.
Modelling of Experimental Data
- Regression of the Pure Component Data
- Prediction of the Binary Adsorption Equilibria
- The Extended Langmuir Model
- The Extended Sips Model
- The Vacancy Solution Model (VSM)
101 | P a g e Table 7 - 8: Model parameters and errors for Langmuir, Sips and VSM models for adsorption data for ethylene on 13X zeolite at low pressure. The Langmuir model is widely used for regression of absorption data of pure components as discussed in Chapter 3. Of the three models selected in this study, the Langmuir model produced the highest average absolute deviation (AAD), 5.03% for ethane at 323 K The Langmuir model overestimates the saturation limit for ethane at both investigated temperatures.
102 | P a g e The Sips model showed a clear improvement over the Langmuir model in the regression of data for ethane. The Langmuir model underestimates the saturation limit for both ethane and ethylene at both temperatures studied. The least squares error tolerances used in the MATLAB code were significantly higher for the VSM model (10-4) compared to the Langmuir and Sips models (10-9).
Three methods were used to predict binary adsorption equilibria using the extended Langmuir model. Three approaches were used, namely: individual saturation limits, concentration-weighted saturation limit, and algebraic mean for the saturation limit. The convergence criteria are the same as for the extended Langmuir model, see Figures 7–11; the only difference is the model equation.
109 | P a g e Table 7 - 12: Model parameters and errors for the Extended Sips model for the prediction of binary adsorption equilibria of ethane/ethylene on zeolite 13X at 323 K and 1.378 bar.
Conclusions
Recommendations
The volume of the adsorbed phase is much smaller than the volume of gas in the adsorptive phase, therefore:. The partial molar entropy of the ideal vapor phase is given by: where 𝑆𝑔0 is the molar entropy of the vapor in the standard state at pressure P0 Combination of Eq. Conventional volumetric apparatus involved manipulation of pressure by changing the number of moles of gas present in the adsorption cell.
The temperature (Ti1) and pressure (Pi1) of the storage cell as well as the temperature (Ti2, Ti3) and pressure (Pi2) of the equilibrium cell were recorded. The temperature (Tf1) and pressure (Pf1) of the storage cell as well as the temperature (Tf2, Tf3) and pressure (Pf2) of the equilibrium cell were recorded. The uncertainty in the measured mass of gas introduced by the accuracy of the balance.
The method according to Shi et al. 2007) is used to determine the uncertainty in the vapor pressure measurement. What remains is to determine the uncertainty in the adsorbed quantity, q, using the law of propagation of uncertainty. The standard has an uncertainty of 0.03 K. The combined standard uncertainty in temperature is given by:.
Applying the law of propagation of uncertainty, the uncertainty in the number of moles initially present in the storage cell is given by: When charging the equilibrium cell, the same calculations as above were performed for the uncertainty in the number of moles present after charging was present in the storage cell. The uncertainty in the number of moles loaded into the equilibrium cell was calculated as follows:
